Faithful Modeling of Product Lines with Kripke Structures and Modal Logic
Bibliographic record
Abstract
Software product lines are now an established framework for software design.They are specified by special diagrams called feature models.For formal analysis, the latter are usually encoded by Boolean propositional theories.We discuss a major deficiency of this semantics, and show that it can be fixed by considering a product to be an instantiation process rather than its final result.We call intermediate states of this process partial products, and argue that what a feature model really defines is a poset of its partial products.We argue that such structures can be viewed as special Kripke structure that we call partial product Kripke structures, ppKS.To specify these Kripke structures, we propose a CTL-based logic, called partial product CTL, ppCTL.We show how to represent a feature model M by a ppCTL theory ML(M ) (ML stands for modal logic) such that any ppKS satisfying the theory is equal to the partial product line determined by M .Hence, ML(M ) can be considered a sound and complete representation of M .We also discuss several applications of the modal logic view in feature modeling, including refactoring of feature models.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".